Given the functions $f(x) = \sqrt{x+3}$ and $g(x) = 3x$, we want to find $g(f(y))$.

Step 1: Substitute $f(y)$ into $g(x)$.

We know that $f(y) = \sqrt{y+3}$.

So, $g(f(y)) = g(\sqrt{y+3})$.

Step 2: Apply the function $g(x)$.

The function $g(x)$ is defined as $g(x) = 3x$.

Therefore, $g(\sqrt{y+3}) = 3 \times \sqrt{y+3}$.

Final Answer:

$g(f(y)) = 3\sqrt{y+3}$

Would you like more details on any specific part of this process? Here are some related questions you might consider:

1. How do you find $f(g(y))$ if $g(x) = 3x$ and $f(x) = \sqrt{x+3}$?
2. What is the domain of $g(f(y))$?
3. How does the composition of functions work in general?
4. What happens if $f(x) = x^2 + 3$ instead of $\sqrt{x+3}$?
5. How would you find the inverse of $g(f(y))$?

Tip: When dealing with composition of functions, always evaluate the inner function first before applying the outer function.